Chamorro Calendar

The ancient Chamorros measured the year from harvest to harvest. According to Cunningham (1992), Sakkan (year) means harvest. He said that the year was divided into thirteen moons, and that each moon seems to have been associated with something that was happening at that time of year. For instance, he said that Umatalaf was the time to catch red snappers (gatafe). This further reminds me of an interview I had with my father regarding how the full moon is a sign for our Chamorro farmers to pick land crabs, as there would be an abundance that would come out during that time of the day. This was part of a lunar calendar that our people used.

The Ancient Chamorro Calendar included the following:
January: Tumaiguine
February: Maimo
March: Umatalaf – to go catch gataffe (red snapper)
April: Lumuhu – to go back, to return to the attack
May: Makmamao
June: Mananaf or Fananaf
July: Semo
August: Tenhos
September: Lumamlam or Lamlam
October: Fanggualo’ or Fa’gualo – planting time
November: Sumongsong
December: Umayanggan – season of slight but frequent showers
Umagahaf or Omagahaf – to get crayfish


Source:
Cunningham, L.J. (1992). Ancient Chamorro Society. Honolulu, HI: Bess Press.

Mathematics used in Chamorro agriculture

Many Chamorro farmers know that when it’s full moon, the land crabs come out, so it’s the best time to hunt for them. During this time, the female crabs come out in plentiful amounts, and therefore your catch is bound to be a good one.

My father recalls the days when he would hunt for crabs during the time of the full moon and how he and his family would reap the rewards of their bountiful crab hunting. He mentioned of how he would get home with much enthusiasm, and how family members would grind the coconut, boil the coconut milk with the crab, cook hot rice, and then they would all sit down to eat together and count how many crabs they caught.

So what are the mathematics concepts involved in crab hunting? For one thing, the full moon is part of the lunar calendar. Secondly, on the day of the full moon, we are able to see that various living things feel and act differently, such as the case of the crabs that come out during this time. In some cases, the reproductive cycle is in sync with the moon's cycle. As the moon goes through its different phases we can see the different shapes that it takes, including the new moon, crescent moon, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, another crescent, and then another new moon. All of these are concepts of mathematics with the different stages that occur, and that's not including the fun fact of counting how many crabs were actually caught!

Aside from land-crab hunting, there is the clam digging during low tide on our Tapon Dia (Clam Day). Growing up I would go to the beach every weekend with my family to dig for clams. My siblings and I would use our fingers to dig deep into the sand and pick as many clams as we could all day long. We’d often count the amount of clams we each gathered. It was like a contest for us, but that didn’t matter once we reaped the rewards of our efforts. The reward of eating what we had caught was a special time for all of us.

My mother or father would grind the coconut, so that we could boil the clams with coconut milk and eat it with hot rice. I can honestly say that after a hard day’s work, the harvest of clams, and then eating them, was well worth the effort.

Going back to mathematics, what exactly are the mathematics concepts involved in clam harvesting? For one thing, the digging occurs during certain times, most especially when it's low tide. Secondly, the time of the year or particular months/seasons of the year must also be considered. A mathematical formula is also used to determine the number of clams available, and we must be sure to harvest in a way that ensures we do not deplete the standing stock of clams. All of these elements deal with mathematics, and that's not including the fun fact of us counting how many clams we actually harvested!

Source:
Naputi, Joaquin. Personal INTERVIEW. 6 February 2010.

Mathematics Used In Chamorro Medicine

The focus of this is the Suruhana, as island residents sometimes seek the medicinal/spiritual powers of her when they fall ill. In my family the spiritual stories remain alive of my great grandmother, Antonia Chargualaf Nangauta, who served as the Suruhana (female herb doctor) of Malesso (Merizo). My father shared of how she would cure the sick by giving them herbs to eat or drink, or maybe even massage them. Yet he said that when she healed someone, the sickness imposed by the spirit would transfer to her, so she, herself would have to drink herbs to cure herself. He said that she often instructed those inflicted with sickness to visit the site where their illness began and ask for forgiveness for disturbing the spirits.

Both of my parents reminded me that if I should ever enter the jungle to be careful not to disturb the taotaomo'na (ghost; people of before). They mentioned that I must ask for permission from the Guela yan Guelo (grandmother and grandfather) before I begin my travel, so that I may not get sick, pinched, get red marks, or even swell. Although the Suruhana is revered, my mother said that there aren't as many that can be found these days, for they too, grow of old age, just like my great grandmother, who has since passed away.

Mathematics concepts that my great grandmother had to consider include the following: Amount of herbs used, type and texture of herbs used, amount of water to boil herbs, time of preparation of herbal medicine, number and pressure of massages used to heal, and length of massage therapy.

Sources:
Naputi, Joaquin. Personal INTERVIEW. 7 February 2010
Naputi, Julia. Personal INTERVIEW. 7 February 2010

Chamorro Counting System

While researching on the Chamorro counting system, I came across the ancient Chamorro measuring system and measurement of length that I've only heard a few times in my life and only bits and pieces of them. Cunningham (1992) did a good job in explaining these measurements, as shown below.

Measuring System –

Measurement of dry volume

chupa = 1 cup

ganta = 8 cups = one-half gallon

Measurement of length

dedo = length of the second joint of the index finger

hemi = the length from the tip of the index finger to the spread thumb

kodu = the length from the elbow to the end of a clenched fist

kuatta = the length from the end of the thumb to the end of the little finger when the hand is spread

bara = arm length from the shoulder to the end of the fingers

brasa = length from finger tip to finger tip, with both arms outstretched

Source:

Cunningham, L.J. (1992). Ancient Chamorro Society. Honolulu, HI: Bess Press.

Coconut Weaving in the Chamorro Culture

Weaving is said to be a lasting Chamorro artistry. There is mathematics used in the weaving of coconut leaves, for cultural master weavers must count the number of leaves they use, count in patterns, consider the size of the leaves, and dedicate time to the craft being weaved.

My mother is a weaver and has shared with me that leaves have to be wide, so that the craft you make will look more attractive. She said that if the leaves are too skinny it will not cover everything and you will end up having holes in your product.

Among the crafts my mother is able to make within minutes include the following: hat, bird, roses, fan, and headband. She said that it takes about half an hour to weave a hat and bird, 5 minutes to weave 3 roses, 15-20 minutes to weave a fan, and 5 minutes to weave 3 headbands.

She said that the weaving of hats follow a certain pattern, and your counting depends on the size of the hat you wish to make. For instance, the hat for kids would be a smaller size, and it would require about 16 leaves and less counting. On the other hand, the hats for adults would require about 20 leaves and more counting.

My mother said that the headband requires 3 leaves to make, and you would simply adjust it to fit either the child or adult. She said that the bird and rose each require one leaf to make.

She said that counting is especially important when making hats and fans. “You have no choice but to count,” she said. “The fan could be any size, either big or small, but no matter the size, you still have to count on each side for the fan.”

When asked why she enjoys weaving, my mother said that it “feels good and it’s therapeutic. I’m happy knowing that I’m sharing my gift with others.” I am touched by her words, and indeed, I agree that there’s no better reward than knowing that you have made a difference in some way or another. Moreover, I am a teacher because I also want to make a difference, one student at a time!

Source:
Naputi, Julia. Personal INTERVIEW. 6 February 2010.

Mathematics used in farming in the Chamorro culture

For Assignment #3, we were tasked to further specify the mathematics concepts used in our topics. Coming from a family of farmers, I've decided to expand on the mathematics used in farming in the Chamorro culture. If you don't know by now, my father is a farmer, and his father was a farmer, and his father's father was a farmer, and so on. My father shared with me that when you farm, you must consider the distance feet between hills (i.e. plants planted two per hill), the number of plants per hill, the distance feet between rows, the number of plants/100 ft. row, the number of plants per acre, 100 ft. row yield (lb.), and eventually, you'll have to figure out the estimated cost per 100 ft. row, per acre yields (lbs.), estimated cost per acre, and the breakeven price. The University of Guam Cooperative Extension Service has also researched and provided outreach to farmers on the elements I've mentioned.

For instance, the following is a breakdown provided by the UOG Cooperative Extension Service for eating and cooking bananas.

Recommended distance ft. between hills - 10
Recommended no. plants per hill - 1
Recommended distance ft. between rows - 12
No. plants/100 ft. row - 10
No. plt./acre - 363
100 ft. row yield (lb.) - 500
Estimated cost per 100 ft. row - $229.75
Per acre yield (lbs) - 17,500
Estimated cost per acre - $8,340
Breakeven price - 48 cents

Just the figures above involve a lot of mathematics, and the more bananas you plant, the more calculating you'll have to engage in! My father stated that although he loves planting bananas, which take about 14 months to grow, once you cut them down after they bear, they do not bear again, compared to other plants. On the other hand, he said that cucumbers tend to bear more, because once they're ready for picking, you would harvest them every other day. Thus, it takes cucumbers 45 days to grow with the harvesting to occur every other day for 2 weeks.

My father mentioned that if you want to plant long-term fruit trees that always bear fruit, you would have to plant any of the following: mango, coconut, star apple, and sour sap. He said that these plants would ensure that you always have something to harvest once they start bearing. However, he also mentioned that these trees take about 7 years or more to bear. Despite this, the beauty is that once they start bearing, they bear non-stop.

My father always encourages fellow farmers to use organic dead leaves and other compost mater to fertilize the plants, so that the plants can "produce better, grow better, and grow healthier."

When asked about his final thoughts on Mathematics in agriculture, he said that "It (mathematics) is important in agriculture, because it tells you what crops can bring you better economic benefits and can sustain your family for the long run." He also mentioned about the hard work, care, and appreciation that goes into the love of farming.

I am grateful that I was able to interview my father. He provided much insight, and I look forward to conducting more research on this, and how it can impact student learning in mathematics for all grade levels.

Sources:
Naputi, Joaquin. Personal INTERVIEW. 5 February 2010.
UOG Cooperative Extension Service

Number Similarities in Pacific Island Languages

Hafa Adai! It is interesting to note that there are number similarities in Pacific Island languages. In fact, this was noted by H. Costenoble's "The Family Tree of Chamorro," and Cunningham (1992) also reported this in his book titled, "Ancient Chamorro Society."

Here's a snapshot of these number similarities:

Note: Click on the image above to get a clearer view.

I look forward to engaging in more research that will provide additional details on the similarities.


References:
Costenoble, H. (1974). The Family Tree of Chamorro. Guam Recorder, 4(2), 25.
Cunningham, L.J. (1992). Ancient Chamorro Society. Honolulu, HI: Bess Press.